Question

Three lines are drawn from the origin $O$ with direction cosines proportional to $(1,-1,1),(2-3,0)$ and $(1,0,3)$ . The three lines are

• A. not coplanar
• B. coplanar
• C. perpendicular to each other
• D. coincident

Answer 1

Answer: (B)

$\Delta =\left|\begin{array}{ccc}1& -1& 1\\ 2& -3& 0\\ 1& 0& 3\end{array}\right|$
$=1(-9-0)-(-1)\cdot (6-0)+1(0-(-3))$
$=-9+6+3=0$
Since, $\Delta =0$
$\therefore$ Lines are coplanar.